Abstract: A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree are the algebraic foci of a curve of class which is tangent to the lines joining pairs of zeroes. We prove the analogous results for hyperbolic polynomials, that is, for Blaschke products with roots in the unit disc.